Compliance Modeling and Analysis of a 3-RPS Parallel Kinematic Machine Module

The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine（PKM） as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform＇s compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform＇s compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.

Compliance Modeling of a Compliant Stage with Symmetric Configuration

This paper presents the compliance modeling of a compliant stage with symmetric configuration. Empirical compliance equations for the circular flexure hinge are first introduced. Using the matrix method, the output compliance of a compliant stage with symmetric configuration is then obtained. Finally, the compliances derived from the proposed theoretical model and finite element analysis (FEA) are compared. It indicates that the results calculated by the theoretical model are in good agreement with those derived from FEA, which demonstrates the accuracy of the theoretical model.

Compliance Analysis of a 3-DOF Spindle Head by Considering Gravitational Effects

The compliance modeling is one of the most significant issues in the stage of preliminary design for parallel kinematic machine（PKM）. The gravity ignored in traditional compliance analysis has a significant effect on pose accuracy of tool center point（TCP） when a PKM is horizontally placed. By taking gravity into account, this paper presents a semi-analytical approach for compliance analysis of a 3-DOF spindle head named the A3 head. The architecture behind the A3 head is a 3-RPS parallel mechanism having one translational and two rotational movement capabilities, which can be employed to form the main body of a 5-DOF hybrid kinematic machine especially designed for high-speed machining of large aircraft components. The force analysis is carried out by considering both the externally applied wrench imposed upon the platform as well as gravity of all moving components. Then, the deflection analysis is investigated to establish the relationship between the deflection twist and compliances of all joints and links using semi-analytical method. The merits of this approach lie in that platform deflection twist throughout the entire task workspace can be evaluated in a very efficient manner. The effectiveness of the proposed approach is verified by the FEA and experiment at different configurations and the results show that the discrepancy of the compliances is less than 0.04 μm/N^-1 and that of the deformations is less than 10μm. The computational and experimental results show that the deflection twist induced by gravity forces of the moving components has significant bearings on pose accuracy of the platform, providing an informative guidance for the improvement of the current design. The proposed approach can be easily applied to the compliance analysis of PKM by considering gravitational effects and to evaluate the deformation caused by gravity throughout the entire workspace.

Torque estimation for robotic joint with harmonic drive transmission based on system dynamic characteristics

In the applications of joint control and robot movement,the joint torque estimation has been treated as an effective technique and widely used.Researches are made to analyze the kinematic and compliance model of the robot joint with harmonic drive to acquire high precision torque output.Through analyzing the structures of the harmonic drive and experiment apparatus,a scheme of the proposed joint torque estimation method based on both the dynamic characteristics and unscented Kalman filter(UKF)is designed and built.Based on research and scheme,torque estimation methods in view of only harmonic drive compliance model and compliance model with the Kalman filter are simulated as guidance and reference to promote the research on the torque estimation technique.Finally,a promoted torque estimation method depending on both harmonic drive compliance model and UKF is designed,and simulation results compared with the measurements of a commercial torque sensor,have verified the effectiveness of the proposed method.

Preliminarily modeling of creep effect in electro-dynamic loudspeaker suspensions

The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid（FSLS） model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid（SLS） model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.

Characteristics of Statically Indeterminate Symmetric Flexure Structures

Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.